Ok, so I'm in a 1E game, with a mind controller named Vixxxen. Now, one of the other characters slapped her on the butt, so she put him under her control. This all worked fine. However, the player and I have a disagreement on the way the control aspect works.

The rules clearly state that to order a controlled person around, you have to make a power check with DC 10 or 15, plus the character's will save bonus.

However, the player disagrees, saying that the controlled character should roll a will save (1d20+bonus) and then add 10 or 15 to that to set the DC. WHich one is correct?

You are right, he is wrong. You do not add an additional 10 or 15 to the save the target is making.

Mind Control DC is the base command category difficulty plus the target's Will save/bonuses combined.

Each command needs to see a power check by the attacker meet the DC target (does not have to be over the DC). See 76 last sentence before the chart).

Target must speak the same language as the target of the effect, his words have to be heard, and the controller must see the target he hopes to control (so if you are blinded, you are screwed). Simple commands CAN be given through gesture (GMs call).

Ex:
If MINDWHIP (has mind control +8 or 8 ranks) tries to control IRONHORSE (strong tuff hero with Amazing Save: WiLL +4, and a Wisdom of 12) with the intent of forcing him to run off of the roof of the building they are fighting on. After all, MINDWHIP has taken some hits in combat & isn't going to make it another 2 rounds.

(GM) rules that 'running off of a roof' would be an action that Ironhorse would be strongly opposed to doing (which means base DC 15, plus + 4DC(Ironhorse's Amazing Save: WiLL) and another +1 DC from WIS modifier.

So the total is DC 15+4+1 = Total DC 20. Everytime MINDWHIP wants IRONHORSE to do something he is 'strongly opposed' to now requires a spoken command or gesture and a modified roll of at least 20 (roll+rank+misc).

Given that MINDWHIP has Mind Control +8, he only needs to roll a 12 on a d20 to succeed at the attempt (DC20 - 8 ranks of mind control= 12).

MINDWHIP can as a half action increase his hold on the mind of IRONHORSE. Such attempts grant an additional Will save to the target of the Mind Control, which now faces the task of rolling over the controller's (in the case MINDWHIP's power = DC 10+8 ranks= 18 DC).

MMDx
"Tell me what's on your mind, or I'll find out for myself"--Kitron Kayle in Swaptown to Tamath Wolfhart
"Tell me what's on your mind, friend ... lest I see for myself."